Answer:
[tex]=\frac{81m^2n^5}{8}[/tex]
Step-by-step explanation:
One is given the following expression:
[tex]\frac{(3m^-^1n^2)^4}{(2m^-^2n)^3}[/tex]
Simplify, distribute the exponent outside of the parenthesis by the terms inside of it. Remember, when a value that already has an exponent is raised to another exponent, the equivalent of these two values is multiplying the exponents together. Use this property here:
[tex]=\frac{(3m^-^1n^2)^4}{(2m^-^2n)^3}[/tex]
[tex]=\frac{3^4m^(^-^1^)^(^4^)n^(^2^)^(^4^)}{2^3m^(^-^2^)^(^3^)n^3}[/tex]
[tex]=\frac{81m^-^4n^8}{8m^-^6n^3}[/tex]
Now simplify this fraction. Keep in mind that a fraction is another way of representing the operation of division. When one wants to divide terms raised to an exponent, one must make sure that these terms have a like base. Then one will subtract the exponents from each other. Do this step with terms that have a variable base:
[tex]=\frac{81m^-^4n^8}{8m^-^6n^3}[/tex]
[tex]=\frac{81m^(^-^4^)^-^(^-^6^)n^(^8^)^-^(^3^)}{8}[/tex]
[tex]=\frac{81m^-^4^+^6n^8^-^3}{8}[/tex]
[tex]=\frac{81m^2n^5}{8}[/tex]
